Now here's the thing. Why are these latter verbs exceptions? After all if the verb is 'facio' then surely you can just say that the stem ends in -i as opposed to, say, 'g' as in rego. What is the point of defining as an exception a verb which if we just regard the part before the ending as the end of the stem...is perfectly regular.....?

Also what does Orberg mean by singling out '-o' et '-unt' when this verb has 'i' before all of its endings in the present tense...?

Is the point here that facio, facere doesn't have an i in the infinitive...and so the stem cannot be said to end in 'i'? I see that 'i' makes appearances in this verb depending upon tense etc... so I suppose the stem ends in 'c'...

The verbs you've given are all a subclass of 3rd conjugation called "-io conjugation"(that's their ending in 1st person singular). They largely decline like 3rd conjugation verbs, but have some "irregularites" they all share.And you cannot say their stems end in "i" because that'd make them a part of 4th conjugation, which they do not follow.